Question

In a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let p hat Subscript Upper F and p hat Subscript Upper S be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class.

Which of the following is the mean of the sampling distribution of p hat Subscript Upper F Baseline minus p hat Subscript s ?

–0.52
0.52
0.63
1.26.


answer a

Answer 1

The mean of the sampling distribution of the difference between the sample proportions of teachers and students who believe that five minutes is not enough time for students to change classes can be calculated as follows:

mean = p_1 - p_2

where p_1 is the true proportion of teachers who believe that five minutes is not enough time for students to change classes, and p_2 is the true proportion of students who believe the same.

We can estimate p_1 and p_2 using the sample proportions of teachers and students who believe that five minutes is not enough time for students to change classes:

p_hat_1 = (proportion of teachers in the sample who believe that 5 minutes is not enough) = 0.37
p_hat_2 = (proportion of students in the sample who believe that 5 minutes is not enough) = 0.89

Then, the mean of the sampling distribution of p_hat_1 - p_hat_2 is:

mean = p_hat_1 - p_hat_2
= 0.37 - 0.89
= -0.52

Therefore, the mean of the sampling distribution of p_hat_1 - p_hat_2 is -0.52. The answer is (a).